Smooth trajectory control of robotic manipulators based on minimum acceleration criterion

Comparing Combinations of Linear and Nonlinear Feedback Terms for Motion Control of Marine Surface Vessels

Robust trajectories following control of a 2-link robot manipulator via coordinate transformation for manufacturing applications

A formal solution to a countable system of second-order differential equations with a small parameter of fractional rank in the derivative is constructed for both resonant and non-resonant cases. Its asymptotic behavior is investigated using the «reduction» method of the countable system of differential equations. The aim of the article is to determine the conditions under which a countable system of second-order linear differential equations with a small parameter of fractional rank in the derivative admits a solution; to construct a formal solution and to prove its asymptotic nature.

A direct-drive motor is an attractive actuator for a robot manipulator because of its high driving torque and accurate positioning abilities. The motion of a robot manipulator driven by a direct-drive motor is, however, strongly affected by inertial forces and nonlinear forces such as coliolis and centrifugal forces because it does not have any transmission mechanisms. It is, therefore, necessary to dynamically control the torque of the direct-drive motors in order to attain accurate motion of the robot manipulator. In this paper, the dynamics of a five-bar-link parallel direct-drive robot manipulator are analyzed. The torque control curves of the direct-drive motors for a three dimensional robot manipulator are derived. A new feedback method (learning control) is adopted, and the effects of the learning control on the motion of the direct-drive robot manipulator are investigated. The robot manipulator must be effective for machining and assembly when the torque is controlled with high accuracy.

A discrete-time learning control for robotic manipulators is studied using its pulse transfer function. Firstly, the discrete-time learning stability condition which is applicable to single-input two-outputs systems is derived. Secondly, the stability of the learning algorithm with a position signal is studied. In this case, when the sampling period is small, the algorithm is not stable because of an unstable zero of the system. Thirdly, the stability of the algorithm with position and velocity signals is studied. In this case, we can stabilize the learning control system which is unstable in the case of learning with only the position signal. Finally, simulation results on the trajectory control of robotic manipulators using the discrete-time learning control are shown. The simulation results agree well with the analytical results.

A discrete-time learning control for robotic manipulators is studied from a viewpoint of zeros of a control system. The signal used for learning is a position signal of each joint detected by a pulse encoder. Firstly, we show that when sampling period is small, the learning is unstable because of an unstable zero of the system. Secondly, we show that we can stabilize the learning control system with small sampling period by using a low pass filter, and also show that a tracking error converges not to zero but to a certain value in that case. Finally, experimental results on the trajectory control of robotic manipulators using the discrete-time learning control are shown. These experimental results agree well with the analytical ones.

A regressor-based variable-structure control scheme has been developed for the trajectory control of robot manipulators in the presence of disturbances, parameter variations, and unmodeled dynamics. The method is based on the regressor structure given by J.J.E. Slotine and W. Li, without parameter adaptation. This avoids the requirement of persistency of excitation, and the convergence of the overall transient exponential. The method is robust against a class of state-dependent uncertainties, which may result, for example, from unmodeled dynamics. The problem of chattering is solved by the smoothing control law. It is with respect to a set around the origin, which can be made arbitrarily small. To illustrate the feasibility of this controller, it was implemented using a Motorola M68000 microprocessor on a two-link revolute joint manipulator subjected to a variable payload. Experimental results confirm the validity of accurate tracking capability and the robust performance. >

A Novel Variable Structure Control Scheme for Robot Trajectory Control

It is proved that every projective connection on an -dimensional manifold is locally defined by a system of second-order ordinary differential equations resolved with respect to the second derivatives and with right-hand sides cubic in the first derivatives, and that every differential system defines a projective connection on . The notion of equivalent differential systems is introduced and necessary and sufficient conditions are found for a system to be reducible by a change of variables to a system whose integral curves are straight lines. It is proved that the symmetry group of a differential system is a group of projective transformations in -dimensional space with the associated projective connection and has dimension . Necessary and sufficient conditions are found for a system to admit the maximal symmetry group; basis vector fields and structure equations of the maximal symmetry Lie algebra are produced. As an application a classification is given of the systems of two second-order differential equations admitting three-dimensional soluble symmetry groups.

In tlus work a nonlinear control method is used for the trajectory control of robotic manipulators. In this method, the correct gain values are obtained using an off-line based numerical optimization method. The results obtained are tested on a two link manipulator whose end effector moves along a circular trajectory. The results show that one can obtain very accurate results using this method

In the present paper, we examine the Model Feedback Control System. Since the Model Feedback Control System is simple, the ModeI Feedback ControI System has been applied to many applications such as the trajectory control of robot manipulator, level control of serially connected tanks and so on. Since the control structure of the ModeI Feedback Control System has constrained, it is likely that the Model Feedback Control System can not represent all of stabilizing controllers for the plant. Nothing has been reported whether or not, the ModeI Feedback Control System can represent all of stabilizing controllers. The purpose of the present paper is to give a solution to the question whether or not, all of stabilizing controllers for the plant are written as the Model Feedback Control structure. Since Model Feedback Control System is applied to many minimum phase systems, in the present paper, we especially clarify the relationship between the ModeI Feedback Control System and the parametrization of all stabilizing controllers for the minimum phase system. First, the relationship between the Model Feedback Control system and the parametrization by Glaria and Goodwin is clarified. Next, for the strictly proper system, the relationship between the Model Feedback Control System and the parametrization by Yamada and Moki is presented. Simple design method of the Model Feedback ControI System to specify control characteristics is shown.

Optimal control strategies are very useful in manipulation problems of robots. However, most optimal controls are highly sensitive to plant-parameter variations and disturbances because optimal controls try to pick up exact information from the mathematical models in order to realize the best performance. We recognize that difficulties are involved in exact modeling of plants and prevention of disturbances. Therefore, we need a optimal control method with low sensitivity. The ideas of closed-loop control system design using LQG/TR techniques (linear quadratic Gaussian control with transfer recovery) are discussed in this paper. We combine optimal controls and LQG/TR control into two-degrees-of-freedom control systems to reduce the sensitivities of optimal control strategies. In digital simulations, we obtained excellent results of a two-link manipulator in an optimal time control problem using our method. Some modeling errors and considerable disturbances are allowed in the method. Thus, we can realize good performances in practical manipulation problems using our method.

Design of a digital adaptive algorithm for torque-controlled robotic joints

This paper deals with two types of systems of second-order differential equations with parameters: coupled systems with the boundary conditions of the Sturm–Liouville type and classical systems with Dirichlet boundary conditions. We discuss an Ambosetti–Prodi alternative for each system. For the first type of system, we present sufficient conditions for the existence and non-existence of its solutions, and for the second type of system, we present sufficient conditions for the existence and non-existence of a multiplicity of its solutions. Our arguments apply the lower and upper solutions method together with the properties of the Leary–Schauder topological degree theory. To the best of our knowledge, the present study is the first time that the Ambrosetti–Prodi alternative has been obtained for such systems with different parameters.

In this paper, the problem of the robust optimal control (ROC) for a class of nonlinear systems with uncertainties and external disturbances is studied. For this purpose, the State Dependent Riccati Equation (SDRE) is considered as a solution of the ROC. The proposed method is to transform a robust control problem into an optimal control problem, where the uncertainties and disturbances are reflected in the performance index. Hence, the performance index is selected as an energy function and using the proposed constraints in this paper the Lyapunov stability for this class of nonlinear systems is proved and the robust optimal controller is designed. In order to illustrate the high capability of the ROC method in optimal control of complex systems such as Hyper-chaotic system, the time response of state variables in the proposed method and the Global Robust Optimal Sliding Mode Control (GROSMC) method are compared together. The simulation results show that the time response of state variables in the ROC method is more sufficient than the GROSMC method.